Using a low-energy model, we calculate the energies of the relevant states throughout the fusion protocol, allowing us to set bounds on the operation timescales. For typical parameters in experimentally available superconductor-semiconductor hybrid structures, we estimate that pulses have to be slower than 100 ps. The upper limit is determined by how well we can switch off the coupling to the TSs and by the maximal achievable coupling to the grounded SC via the JJ FET, as well as by overlaps between the island MBSs and quasiparticle poisoning. We expect these timescales to be within the capabilities of standard arbitrary waveform generators and to leave plenty of room for varying the pulses to demonstrate topological protection of the fusion outcome.
During the fusion protocol, the ground state of the island is doubly degenerate, leading to a parity superposition that can be measured as an excess charge in the island \(50\%\)  of the time using standard charge-detection techniques [1]}. We also design a reference experiment where the ground state of the island remains non-degenerate throughout the protocol, leading to a state with a well-defined charge in the island. Finally, we propose a modified cyclic protocol where the excess electron which arises with \(50\%\)  probability for each fusion cycle leads to a pumped charge between the TS leads and the JJ FET. The parameters can be adjusted to make the pumped charge quantized. This cyclic protocol allows the detection of MBS fusion rules based on fast control but slow (DC) measurements. Throughout the paper we use units where \(\hbar =e=1\) .
